Add lost password e2e tests (#50611)

* Add lost password e2e tests

* Add changefile(s) from automation for the following project(s): woocommerce

* Update lost password e2e test

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Co-authored-by: github-actions <github-actions@github.com>

plugins/woocommerce/changelog/50611-add-lost-password-e2e-test

@@ -0,0 +1,4 @@
+Significance: minor
+Type: dev
+
+Add lost password e2e tests

plugins/woocommerce/tests/e2e-pw/tests/merchant/lost-password.spec.js

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+const { test, expect } = require( '@playwright/test' );
+const { admin } = require( '../../test-data/data' );
+
+test.describe( 'Can go to lost password page and submit the form', () => {
+	test( 'can visit the lost password page from the login page', async ( {
+		page,
+	} ) => {
+		await page.goto( '/wp-login.php' );
+		await page.getByRole( 'link', { name: 'Lost your password?' } ).click();
+		expect( page.url() ).toContain( '/wp-login.php?action=lostpassword' );
+		await expect( page.getByText( 'Get New Password' ) ).toBeVisible();
+	} );
+
+	test( 'can submit the lost password form', async ( { page } ) => {
+		await page.goto( '/wp-login.php?action=lostpassword' );
+		await page.getByLabel( 'Username or Email Address' ).click();
+		await page
+			.getByLabel( 'Username or Email Address' )
+			.fill( admin.username );
+		await page.getByRole( 'button', { name: 'Get New Password' } ).click();
+
+		try {
+			await page.waitForURL( '**/wp-login.php?checkemail=confirm' );
+			await expect(
+				page.getByText( /Check your email for the confirmation link/i )
+			).toBeVisible();
+		} catch ( e ) {
+			// For local testing, the email might not be sent, so we can ignore this error.
+
+			// eslint-disable-next-line jest/no-try-expect
+			await expect(
+				page.getByText(
+					/The email could not be sent. Your site may not be correctly configured to send emails/i
+				)
+			).toBeVisible();
+		}
+	} );
+} );